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Strategy and work plan

The workplan for the CRP is a union of workplans of included IPs. However, at the general level we would like to emphasise some integral points.

No lost time. Since we know each other very well and we worked together in several joint papers, there will be no time wasted in the introductory phase.

International cooperation We plan to engage several postgraduate students and several post-docs into this CRP. For instance, a student of Egon Schulte would like to spend some time in Europe as a postdoc in Belgium and Slovenia. There are plans to exchange PhD students between Slovenian and Slovakian team. Austrian universities engaged in this CRP have already hosted several graduate students from Slovenia, Croatia and Turkey.

Higly sophisticated software. Having such a large group of outstanding PIs and APs gives us greater flexibility in forming task groups for achieving particular objectives. Our researchers have proven in the past that they can provide useful algorithms and practical software (Conder - Lowx, Slovenian group - Vege, Batagelj - Pajek [23], Leemans - contribution to Magma, . . . ) Since our researchers are leading in the world it is highly unlikely that such a strong group giving such important results can be formed anywhere else.

Knowledge dissemination. Our past record proves that we are good conference organizers and intend to share the acquired knowledge with others also through the new research journal Ars Mathematica Contemporanea.

Coherent theory of graph representation. Currently there exist partial results in graph representations. By the end of this project we will unite them all and give a coherent theory.

Work in project will hence include renewal and incorporating various software to a common platforms:1. Various censuses of classes of maps, polytopes, graphs, e.g. Wilson census of maps (Orbanić, Potočnik, Pisanski, Brinkmann, Conder).2. Reviving and transporting Vega to Magma, Sage, Python (Pisanski, Bauer, Orbanić, Boben, Conder, Leemans).3. Incorporation of new software to Pajek in order to make it marketable (Batagelj, Horvat, Lukšič, Orbanić).4. Incorporation of new sequences to Sloane’s Encyclopedia of Integer Sequences (Boben, Petkovšek, Pisanski)5. New algorithms for graph representations and drawings (Imrich, Klavžar, Stadler, Žitnik, Boben).